Demodulation that accounts for channel estimation error

ABSTRACT

Methods and apparatus for demodulating data symbols received over a communication channel. One method includes receiving a data symbol y over a communication channel h, where the received data symbol y corresponds to a transmitted data symbol x. The method further includes determining an estimate of the communication channel h. The method further includes determining a measure of a channel estimation error corresponding to the estimate of the communication channel h. The method further includes determining a likelihood value for a bit in the transmitted data symbol y based at least in part on the measure of the channel estimation error.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Patent App. No.61/105,581 entitled “Optimal LLR Calculation Based on Semi-CoherentDetection,” filed on Oct. 15, 2008, the disclosure of which is herebyexpressly incorporated herein by reference.

FIELD OF TECHNOLOGY

The present disclosure relates generally to communication systems and,more particularly, to demodulation that accounts for channel estimationerror.

BACKGROUND

An ever-increasing number of relatively inexpensive, low power wirelessdata communication services, networks and devices have been madeavailable over the past number of years, promising near wire speedtransmission and reliability. Various wireless technology is describedin detail in the 802 IEEE Standards, including for example, the IEEEStandard 802.11a (1999) and its updates and amendments, the IEEEStandard 802.11g (2003), and the IEEE Standard 802.11n now in theprocess of being adopted, all of which are collectively incorporatedherein fully by reference. These standards have been or are in theprocess of being commercialized with the promise of 54 Mbps or higherdata rate, making them a strong competitor to traditional wired Ethernetand the more common “802.11b” or “WiFi” 11 Mbps mobile wirelesstransmission standard.

Generally speaking, transmission systems compliant with the IEEE 802.11aand 802.11g or “802.11a/g” standards as well as the IEEE 802.11nstandard achieve their high data transmission rates using OrthogonalFrequency Division Multiplexing (OFDM) encoded symbols. Generallyspeaking, the use of OFDM divides the overall system bandwidth into anumber of frequency sub-bands or channels, with each frequency sub-bandbeing associated with a respective sub-carrier. Data upon eachsub-carrier may be modulated with a modulation scheme such as QAM, phaseshift keying, etc. Thus, each frequency sub-band of the OFDM system maybe viewed as an independent transmission channel within which to senddata, thereby increasing the overall throughput or transmission rate ofthe communication system.

Generally, transmitters used in the wireless communication systems thatare compliant with the aforementioned 802.11a/802.11g/802.11n standardsas well as other standards such as the 802.16 IEEE Standard, performmulti-carrier OFDM symbol encoding (which may include error correctionencoding and interleaving), convert the encoded symbols into the timedomain using Inverse Fast Fourier Transform (IFFT) techniques, andperform digital to analog conversion and conventional radio frequency(RF) upconversion on the signals. These transmitters then transmit themodulated and upconverted signals after appropriate power amplificationto one or more receivers, resulting in a relatively high-speed timedomain signal with a large peak-to-average ratio (PAR).

Likewise, the receivers used in the wireless communication systems thatare compliant with the aforementioned 802.11a/802.11g/802.11n and 802.16IEEE standards generally include an RF receiving unit that performs RFdownconversion and filtering of the received signals (which may beperformed in one or more stages), and a baseband processor unit thatprocesses the OFDM encoded symbols bearing the data of interest.Generally, the digital form of each OFDM symbol presented in thefrequency domain is recovered after baseband downconversion,conventional analog to digital conversion and Fast FourierTransformation of the received time domain analog signal. Thereafter,the baseband processor performs frequency domain equalization (FEQ) anddemodulation to recover the transmitted symbols. The recovered andrecognized stream of symbols is then decoded, which may includedeinterleaving and error correction using any of a number of known errorcorrection techniques, to produce a set of recovered signalscorresponding to the original signals transmitted by the transmitter.

For ease of explanation, in the examples presented herein, streams andsymbols have a one-to-one correspondence. That is, a single stream isassociated with a single symbol and vice versa. Accordingly, the words“streams” and “symbols” may be used interchangeably. However, it shouldbe understood that a given stream, for example, may have a number ofassociated symbols and vice versa.

In wireless communication systems, the RF modulated signals generated bythe transmitter may reach a particular receiver via a number ofdifferent propagation paths, the characteristics of which typicallychange over time due to the phenomena of multi-path and fading.Moreover, the characteristics of a propagation channel differ or varybased on the frequency of propagation. To compensate for the timevarying, frequency selective nature of the propagation effects, andgenerally to enhance effective encoding and modulation in a wirelesscommunication system, each receiver of the wireless communication systemmay periodically develop or collect channel state information (CSI) foreach of the frequency channels, such as the channels associated witheach of the OFDM sub-bands discussed above. Generally speaking, CSI isinformation defining or describing one or more characteristics abouteach of the OFDM channels (for example, the gain, the phase and the SNRof each channel). Upon determining the CSI for one or more channels, thereceiver may send this CSI back to the transmitter, which may use theCSI for each channel to precondition the signals transmitted using thatchannel so as to compensate for the varying propagation effects of eachof the channels.

To further increase the number of signals which may be propagated in thecommunication system and/or to compensate for deleterious effectsassociated with the various propagation paths, and to thereby improvetransmission performance, it is known to use multiple transmit andreceive antennas within a wireless transmission system. Such a system iscommonly referred to as a multiple-input, multiple-output (MIMO)wireless transmission system and is specifically provided for within the802.11n IEEE Standard now being adopted. Various other standards andprojects, such as the 802.16 standard, or WiMAX, and the Long TermEvolution (LTE) project, support MIMO techniques. Generally speaking,the use of MIMO technology produces significant increases in spectralefficiency and link reliability of IEEE 802.11, IEEE 802.16, and othersystems, and these benefits generally increase as the number of transmitand receive antennas within the MIMO system increases.

In addition to the frequency sub-channels created by the use of OFDM, aMIMO channel formed by the various transmit and receive antennas betweena particular transmitter and a particular receiver may include a numberof independent spatial channels. As is known, a wireless MIMOcommunication system can provide improved performance (e.g., increasedtransmission capacity) by utilizing the additional dimensionalitiescreated by these spatial channels for the transmission of additionaldata. Of course, the spatial channels of a wideband MIMO system mayexperience different channel conditions (e.g., different fading andmulti-path effects) across the overall system bandwidth.

Generally, a wireless communication system in which a transmittingdevice transmits a signal to a receiving device may be represented by amodel such as:y=hx+z,  (1)where y represents the symbol, or symbols, received by the receivingdevice, h represents the communication channel (also referred to as“channel gain”), x represents the symbol, or symbols transmitted by thetransmitting device and z represents noise (e.g., additive Gaussiannoise with power σ_(z) ²). Therefore, when a receiving device receives asymbol y, the receiving device may estimate the symbol x transmitted bythe transmitting device.

The receiving device may estimate the transmitted symbol x using varioustechniques including “hard-decision” techniques and “soft-decision”techniques. Hard techniques typically involve simply making adetermination regarding values of bits in the transmitted symbol x(e.g., whether a given transmitted bit is 0 or 1). Soft-decisiontechniques typically involve calculating likelihood values for thetransmitted bits, where a likelihood value for a given bit indicateswhether that bit is more likely to be 0 or 1. For example, thelikelihood value L(i) for a given bit i in the transmitted symbol x maybe represented by a log-likelihood ratio (LLR) as follows:

$\begin{matrix}{{L(i)} = {\log\frac{P\left( {i = 1} \right)}{P\left( {i = 0} \right)}}} & (2)\end{matrix}$

where P(i=1) is the probability that the bit i is equal to 1 and P(i=0)is the probability that the bit i is equal to 0. Accordingly, if L(i) isa relatively large positive number, the probability that the bit i isequal to 1 is much greater than the probability that the bit i is equalto 0, and it may be determined that the bit i is equal to 1. Likewise,if L(i) is a relatively large negative number, the probability that thebit i is equal to 0 is much greater than the probability that the bit iis equal to 1, and it may be determined that bit i is equal to 0. IfL(i) is neither a large positive number nor a large negative number,additional processing may be necessary to estimate the value of the biti.

As known in the art, the LLR calculation for the bit i expressed inequation (2) may be written as follows:

$\begin{matrix}{{L(i)} = {{\log\frac{\sum\limits_{x \in S_{1,i}}s^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2}}}}{\sum\limits_{x \in S_{0,i}}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2}}}}} = {{\log{\sum\limits_{x \in S_{1,i}}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2}}}}} - {\sum\limits_{x \in S_{0,i}}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2}}}}}}} & (3)\end{matrix}$

where S_(1,i) is a set of all possible data symbols x with the bit iequal to 1 and S_(0,i) is a set of all possible data symbols x with thebit i equal to 0. As is also known in the art, equation (3) may beapproximated using log-max approximation as follows:

$\begin{matrix}{{L(i)} \approx {{\min\limits_{x \in S_{0,i}}{{y - {hx}}}^{2}} - {\min\limits_{x \in S_{1,i}}{{y - {hx}}}^{2}}}} & (4)\end{matrix}$

As indicated by equation (4), the LLR calculation for a given bit i inthe transmitted symbol x depends, in part, on the estimatedcommunication channel h. Various techniques may be used to estimate thecommunication channel h. However, these techniques will typicallyestimate the communication channel h with some degree of error. As aresult, LLR based on h may lead to errors in estimating x.

SUMMARY

The present disclosure provides for demodulating data symbols receivedover a communication channel.

In one embodiment, a method includes receiving a data symbol y over acommunication channel h, where the received data symbol y corresponds toa transmitted data symbol x. The method further includes determining anestimate of the communication channel h. The method further includesdetermining a measure of a channel estimation error corresponding to theestimate of the communication channel h. The method further includesdetermining a likelihood value for a bit in the transmitted data symboly based at least in part on the measure of the channel estimation error.

In various implementations, one or more of the following features may beincluded. The measure of the channel estimation error may be set to amean square error σ_(h) ² of the channel estimation error. The measureof the channel estimation error may also be set to a noise power σ_(z)².

Determining the likelihood value for the bit in the transmitted datasymbol may include calculating a log-likelihood ratio for the bit.Determining the likelihood value for the bit may include calculating

$\begin{matrix}{{L(i)} = {\log\frac{\sum\limits_{x \in S_{1,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}{\sum\limits_{x \in S_{0,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}}} & (5)\end{matrix}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to 0, and σ_(h) ² is a mean square error ofthe channel estimation error.

Furthermore, calculating the likelihood value for the bit may includecalculating

$\begin{matrix}{{{L(i)}{\max\limits_{x \in S_{1,i}}{\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}}} - {\underset{x \in S_{0,i}}{\max\;}\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}} & (6)\end{matrix}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to 0, and σ_(h) ², is a mean square error ofthe channel estimation error.

In another embodiment, a method includes receiving a data symbol y overa communication channel h, where the received data symbol y correspondsto a transmitted data symbol x. The method further includes determininga measure of noise on the communication channel h. The method furtherincludes determining a likelihood value for a bit in the transmitteddata symbol x based at least in part on the measure of noise on thecommunication channel h.

In various implementations, one or more of the following features may beincluded. Determining the likelihood value for the bit in thetransmitted data symbol x may include calculating a log-likelihood ratiofor the bit. The measure of noise on the communication channel h may beset to a noise power σ_(z) ².

In another embodiment, an apparatus includes a demodulator and adecoder. The demodulator configured to receive a data symbol y over acommunication channel h, where the received data symbol y corresponds toa transmitted data symbol x. The demodulator is further configured todetermine an estimate of the communication channel h. The demodulator isfurther configured to determine a measure of a channel estimation errorcorresponding to the estimate of the communication channel h. Thedemodulator is further configured to determine a likelihood value for abit in the transmitted data symbol x based at least in part on themeasure of the channel estimation error. The decoder is configured todecode the received data symbol y based at least in part on thecalculated likelihood value.

In various implementations, one or more of the following features may beincluded. The measure of the channel estimation error may be set to amean square error σ_(h) ² of the channel estimation error. The measureof the channel estimation error may be also set to a noise power σ_(z)².

The demodulator may be configured to determine the likelihood value forthe bit in the transmitted data symbol by calculating a log-likelihoodratio for the bit. Calculating log-likelihood ratio for the bit mayinclude calculating

$\begin{matrix}{{L(i)} = {\log\frac{\sum\limits_{x \in S_{1,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}{\sum\limits_{x \in S_{0,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}}} & (7)\end{matrix}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to 0, and σ_(h) ² is a mean square error ofthe channel estimation error.

The demodulator may also be configured to determine the likelihood valuefor the bit by calculating

$\begin{matrix}{{{L(i)}{\max\limits_{x \in S_{1,i}}{\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}}} - {\underset{x \in S_{0,i}}{\max\;}\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}} & (8)\end{matrix}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to 0, and σ_(h) ² is a mean square error ofthe channel estimation error.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example single-stream wirelesscommunication system that may utilize demodulation techniques describedherein;

FIG. 2 is a block diagram of an example transmitting device that may beused in the single-stream wireless communication system of FIG. 1;

FIG. 3 is an example constellation set for a 16-QAM scheme;

FIG. 4 is a block diagram of an example receiving device that mayutilize demodulation techniques described herein;

FIG. 5 is a flow diagram of an example demodulation technique thataccounts for channel estimation error that may be used in asingle-stream wireless communication system;

FIG. 6 is a block diagram of an example multi-stream wirelesscommunication system that may utilize demodulation techniques describedherein;

FIG. 7A is a block diagram of an example transmitting device that may beutilized in the multi-stream wireless communication system of FIG. 6;

FIG. 7B is a block diagram of another example transmitting device thatmay be utilized in the multi-stream wireless communication system ofFIG. 6;

FIG. 8 is a block diagram of an example receiving device that mayutilize demodulation techniques described herein;

FIG. 9 is a flow diagram of an example demodulation technique thataccounts for channel estimation error that may be used in a multi-streamwireless communication system; and

FIG. 10 is a graph illustrating the performance of a simulated receivingdevice utilizing conventional demodulating techniques and theperformance of a simulated receiving device utilizing demodulationtechniques described herein.

When individual elements are designated by references numbers in theform Xn, these elements may be referred to in the collective by X.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of an example wireless communication system100 in which multiple devices, e.g., a transmitting device 102 and areceiving device 106, may communicate with each other via a sharedwireless communication channel 104. Each of the devices 102 and 106 maybe, for example, a stationary device, such as a base station or a mobilestation. Although the wireless communication system 100 illustrated inFIG. 1 includes two devices, the wireless communication system 100 may,of course, include any number of devices.

Furthermore, although the wireless communication system 100 illustratedin FIG. 1 includes a transmitting device 102 and a receiving device 106,devices in the wireless communication system 100 may generally operatein multiple modes (e.g., a transmit mode and a receive mode). Forexample, if a given device is a mobile station in a WiMAX communicationnetwork or a lap top computer having an IEEE Standard 802.11n compliantwireless transceiver, the device may operate in both a transmit mode anda receive mode.

The transmitting device 102 and the receiving device 106 may communicateusing a single frequency or multiple frequencies. When the transmittingdevice 102 and the receiving device 106 communicate using a multiplefrequencies, the communication channel 104 may include multiple carriersor subcarriers, each associated with a particular frequency at which thedevices 102 and 106 may communicate. In some embodiments, the wirelesscommunication system 100 may use an OFDM technique, and the subcarriersmay be selected to be mutually orthogonal (i.e., to minimize cross-talkbetween each pair of subcarriers). However, the wireless communicationsystem 100 could also use any other frequency division multiplexingtechnique.

The receiving device 106 may be configured to perform demodulationtechniques that account for channel estimation error, which will bedescribed in more detail below. Before describing the demodulationtechniques in detail, it is helpful to briefly explain how signals maybe modulated.

FIG. 2 is a block diagram of an example transmitting device 200. Thetransmitting device 200 may be utilized in the wireless communicationsystem 100 as the transmitting device 102, for example. It will beunderstood, however, that the wireless communication system 100 mayalternatively use another transmitting device 102.

Referring to FIG. 2, the transmitting device 200 may generally convert asequence of W information bits b₁, b₂, . . . , b_(W) into signalsappropriate for transmission through a wireless channel (e.g., channel104). More specifically, the transmitting device 200 may include anencoder 220 (e.g., a convolution encoder, a forward error correction(FEC) encoder, and so on) that encodes W information bits b₁, b₂, . . ., b_(W) into Q encoded bits r₁, r₂, . . . , r_(Q), and a modulator 230that modulates the Q encoded bits r₁, r₂, . . . , r_(Q) into datasymbols, which are mapped and converted to signals appropriate fortransmission, e.g., via one or more transmit antennas.

The transmitting device 200 may include various additional modules that,for ease of explanation, are not shown in FIG. 2. For example, thetransmitting device 200 may include an interleaver that interleaves theencoded bits to mitigate burst errors. The transmitting device 200 mayfurther include an analog radio frequency (RF) front end for performingfrequency upconversion, various filters, power amplifiers, and so on.

In some embodiments, the modulator 230 may use QAM to map bits tosymbols in a QAM signal constellation set, where the symbols aredifferentiated from one another by phase and magnitude. For example,FIG. 3 illustrates a 16-QAM constellation set 300 in an in phase andquadrature phase plane. Each constellation point 304 represents adifferent four-bit symbol: 304 a may represent “1101,” 304 b mayrepresent “1100,” 304 c may represent “1110,” 304 d may represent“1111,” and so on. However, other bit to symbol mappings may beutilized.

In general, an n-bit symbol x may be mapped according to an M-QAM signalset, where M=2^(n). Thus, as illustrated in FIG. 3, if the modulator 230uses the 16-QAM modulation scheme the modulator 230 will have a signalalphabet size of M=2⁴=16 (i.e., 16 constellation points), and will map4-bit pairs into the 16 constellation points. If the modulator 230 usesa 64-QAM scheme, the modulator 230 will have an alphabet size of M=2⁶=64(i.e., 64 constellation points) and will map 6-bit segments into the 64constellation points.

FIG. 4 is a block diagram of an example receiving device 400 thatdemodulates received symbols using a technique that accounts for channelestimation error. The receiving device 400 may be utilized in thewireless communication system 100 as the receiving device 106, forexample. It will be understood, however, that the wireless communicationsystem 100 may alternatively use another receiving device 106.Similarly, the receiving device 400 may receive and demodulate multiplestreams transmitted by a device such as the transmitting device 200 ofFIG. 2 or some other transmitting device.

Generally speaking, the receiving device 400 may receive information anddemodulate and decode the received information to estimate theinformation that was sent by a transmitting device. The receiving device400 processes received information utilizing a model, such as:y=(h+Δh)x+z,  (9)where y represents the symbol, or symbols, received by receiving device,x represents the symbol, or symbols, transmitted by the transmittingdevice, z represents noise (e.g., additive Gaussian noise with powerσ_(z) ²), h represents the estimated communication channel, and Δhrepresents the channel estimation error. The channel estimation error Δhmay have a Gaussian distribution with mean square error σ_(h) ² given byσ_(h) ² =E{|Δh| ²}  (10)

The receiving device 400 includes a demodulator 442 that may provide,based on the received data symbols y, likelihood values L(1), L(2), . .. , L(Q) for the transmitted bits r₁, r₂, . . . , r_(Q). The receivingdevice 400 also includes a decoder 444 that may use the likelihoodvalues L(1), L(2), . . . , L(Q) provided by the demodulator 442 toestimate the transmitted bits r₁, r₂, . . . , r_(Q) and, in turn, theoriginal information bits b₁, b₂, . . . , b_(W).

In order to provide likelihood values L(1), L(2), . . . , L(Q) for thetransmitted bits r₁, r₂, . . . , r_(Q), the demodulator 442 may includea likelihood value calculator 454 that calculates the likelihood valuesL(1), L(2), . . . , L(Q) based at least in part on the received symbol yand on the estimated communication channel h. To estimate thecommunication channel h, the demodulator 442 may include a channelestimator 448. Additionally, unlike conventional demodulators, thedemodulator 442 illustrated in FIG. 4 may include a measure of channelestimation error generator 447 that generates a measure of the channelestimation error Δh so that the demodulator 442 may account for thaterror when calculating the likelihood values L(1), L(2), . . . , L(Q).Because channel estimation error Δh may depend on the noise z on thechannel, the demodulator 442 may further include a noise estimator 446for generating noise estimate information, including, for example, thevariance of the noise σ_(z) ².

The demodulator 442, in some embodiments, or in some modes of operation,may not include one or more of the modules 446-454 or, alternatively,may not use each of the modules 446-454 in demodulating the receivedsignals. Further, it will be appreciated that some of the modules446-454 may be combined. Still further, the demodulator 442 and/or thereceiving device 400 may include additional components and/or modulesthat, for ease of explanation, are not shown in FIG. 4. For example, thereceiving device 400 may include a deinterleaver that rearrangesscattered bits and restores the proper bit sequence, an analog RF frontend that performs frequency downconversion, various filters, poweramplifiers, and so on.

Different components and/or modules of the receiving device 400 may beimplemented as hardware, a processor executing software instructions, aprocessor implementing firmware instructions, or some combinationthereof. For example, some or all of the components may be customintegrated circuits, application-specific integration circuits (ASICs),etc., communicatively coupled by electrical busses. In this case, thereceiving device 400 optionally may include bypass busses (not shown) tobypass some of the components if the currently active mode does notrequire certain operations, such as processing multiple presentations ofa symbol encoded according to a space-time encoding scheme.

FIG. 5 is a flow diagram of an example demodulation method 500 that thereceiving device 400, or a similar receiving device, may use tocalculate the likelihood values L(1), L(2), . . . , L(Q) of thetransmitted bits r₁, r₂, . . . , r_(Q), accounting for channelestimation error Δh. For ease of explanation, FIG. 5 will be describedwith reference to FIGS. 1-4. It will be understood, however, that themethod 500 for calculating LLRs may be utilized with systems, devices,and modulation schemes other than those illustrated in FIGS. 1-4.

The receiving device 400 may receive, over a communication channel h, adata symbol y corresponding to a transmitted data symbol x, e.g.,transmitted by a transmitting device (block 510). In order to demodulateand decode the received symbol, the receiving device 400 may firstdetermine an estimate of the communication channel h (block 520), e.g.,using the channel estimator 448. This estimation of the communicationchannel h may be performed in a variety of ways, including using channelestimation techniques known in the art (e.g., least squares channelestimation, iterative channel estimation, and so on).

The receiving device 400 may then generate a measure of the channelestimation error Δh (block 530), e.g., using measure of estimation errorgenerator 447. In one implementation, it may be assumed that the channelestimation error Δh has a Gaussian distribution with a mean square errorσ_(h) ², given by σ_(h) ²=E{|Δh|²} Additionally, σ_(h) ² may beestimated as the noise power, σ_(z) ². In this implementation, themeasure of the channel estimation error Δh may be set to the noisepower. One of ordinary skill in the art, however, will understand thatthe measure of the channel estimation error Δh may be generateddifferently in other implementations. For example, the measure of thechannel estimation error Δh may be set to a scaled value of the noisepower, and the scaling may depend on such facts as the channelestimation technique, the number of training symbols transmitted for thepurpose of channel estimation, etc.

Once the receiving device 400 generates the measure of the channelestimation error Δh (block 530), the receiving device 400 may determinelikelihood values for the bits in the transmitted symbol x using thegenerated measure (block 540), e.g., using the likelihood valuecalculator 454.

For example, in one implementation in which the measure is set to thenoise power, the demodulator 442 may calculate a log-likelihood ratio(LLR) for some, or all, of the Q transmitted bits r₁, r₂, . . . , r_(Q).The LLR of a given bit i may be an indication of whether the bit i ismore likely to be 0 or 1. LLR for a given bit i may be calculated asfollows:

$\begin{matrix}{{L(i)} = {\log\frac{\sum\limits_{x \in S_{1,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}{\sum\limits_{x \in S_{0,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}}} & (11)\end{matrix}$where S_(1,i) is a set of all possible data symbols x with bit i equalto 1 and S_(0,i) is a set of all possible data symbols x with bit iequal to 0. As explained above, if L(i) is a relatively large positivenumber, the probability that the bit i is equal to 1 is much greaterthan the probability that the bit i is equal to 0, so the decoder 444may determine that the bit i is equal to 1. Likewise, if L(i) is arelatively large negative number, the probability that the bit i isequal to 0 is much greater than the probability that the bit i is equalto 1, and the decoder 444 may determine that the bit i is equal to 0. IfL(i) is neither a large positive number nor a large negative number, thedecoder 444 may need to perform additional processing to estimate thevalue of bit i.

Using log-max approximation, equation (11) may be approximated asfollows:

$\begin{matrix}{{{L(i)}{\max\limits_{x \in S_{1,i}}{\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}}} - {\underset{x \in S_{0,i}}{\max\;}\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}} & (12)\end{matrix}$

Therefore, as compared to the LLR calculations in equation (3)-(4), theLLR calculation for the bit i in accordance with equations (11)-(12) isa function of the mean square error σ_(h) ² of the channel estimationerror Δh (e.g., the noise power σ_(z) ²). This compensation for thechannel estimation error Δh may lead to better accuracy in the aggregateassociated with LLR calculation and, more generally, to a more optimalperformance in the aggregate.

Demodulation techniques that account for channel estimation error havebeen described in reference to a single-stream communication system,such as the communication system 100 illustrated in FIG. 1. However, itwill be understood that the techniques described herein may be utilizedwith multi-stream communication systems.

For example, FIG. 6 is a block diagram of an example multi-streamwireless communication system 600 in which multiple devices, e.g., atransmitting device 602 and a receiving device 606 may communicate witheach other via a shared wireless communication channel 604. Each of thedevices 602 and 606 may be, for example, a stationary device, such as abase station or a mobile station equipped with a set of antennas 610-614and 620-624, respectively. Although the multi-stream wirelesscommunication system 600 illustrated in FIG. 6 includes two devices, themulti-stream wireless communication system 100 may, of course, includeany number of devices, each equipped with the same or a different numberof antennas (e.g., 1, 2, 3, 4 antennas and so on).

Furthermore, although the wireless communication system 600 illustratedin FIG. 6 includes a transmitting device 602 and a receiving device 606,devices in the wireless communication system 600 may generally operatein multiple modes (e.g., a transmit mode and a receive mode). Forexample, if a given device is a mobile station in a WiMAX communicationnetwork or a lap top computer having an IEEE Standard 802.11n compliantwireless transceiver, the device may operate in both a transmit mode anda receive mode. Accordingly, in some embodiments, antennas 610-614 and620-624 may support both transmission and reception. Alternatively, oradditionally, a given device may include separate transmit antennas andseparate receive antennas.

Different numbers of spatial streams 630 may be transmitted between theantennas 610-614 and 620-624 in various embodiments and/orconfigurations of the transmitting device 602 and/or the receivingdevice 606. Typically, the number S of spatial streams 630 associatedwith a shared communication channel 606 is less than or equal to minimumof the number N_(T) of transmit antennas 610-614 and the number N_(R) ofreceive antennas 620-624 (i.e., N_(S)≦min(N_(T), N_(R))). The streams630 may be defined in a variety of ways, e.g., according to variousmultiple-input and multiple-output (MIMO) modes or schemes, includingthose known in the art. For example, the transmitting device 602 may usethe antennas 610-614 to improve channel diversity by transmittingmultiple copies of the same symbol via several streams. Alternatively,the transmitting device 602 may transmit different symbols via each ofthe antennas 610-614 to increase throughput. As yet another alternative,the transmitting device 602 may operate in a mixed MIMO mode to improveboth channel diversity and throughput.

The transmitting device 602 and the receiving device 606 may communicateusing a single frequency or multiple frequencies. When the transmittingdevice 602 and the receiving device 606 communicate using multiplefrequencies, the communication channel 604 may include multiple carriersor subcarriers, each associated with a particular frequency at which thedevices 602 and 606 may communicate. In some embodiments, themulti-stream wireless communication system 600 may use an OFDMtechnique, and the subcarriers may be selected to be mutually orthogonal(i.e., to minimize cross-talk between each pair of subcarriers).However, the multi-stream wireless communication system 600 could alsouse any other frequency division multiplexing technique.

The receiving device 606 may be configured to perform demodulationtechniques that account for channel estimation error to be described inmore detail below. Before describing these demodulation techniques indetail, it is helpful to briefly explain how signals may be modulated ina multi-stream communication system.

FIGS. 7A-7B are block diagrams of example transmitting devices 700. Thetransmitting devices 700 may be utilized in the multi-stream wirelesscommunication system 600 as the transmitting device 602, for example. Itwill be understood, however, that the multi-stream wirelesscommunication system 600 may alternatively use another transmittingdevice 102.

Referring to FIG. 7A, the transmitting device 700 a may generallyconvert a sequence of information bits into signals appropriate fortransmission through a wireless channel (e.g., channel 604). Morespecifically, the transmitting device 700 a may include an encoder 720 a(e.g., a convolution encoder, a forward error correction (FEC) encoder,and so on) that encodes information bits, and a modulator 730 a thatmodulates the encoded bits into data symbols, which are mapped andconverted to signals appropriate for transmission via transmit antennas710 a-718 a. The transmitting device 700 a may include variousadditional modules that, for ease of explanation, are not shown in FIG.7A. For example, the transmitting device 700 a may include aninterleaver that interleaves the encoded bits to mitigate burst errors.The transmitting device 700 a may further include an analog radiofrequency (RF) front end for performing frequency upconversion, variousfilters, power amplifiers, and so on.

The modulator 730 a may include a bit-to-symbol mapper 732 a that mapsencoded bits into multiple data symbols, and a symbol-to-stream mapper734 a that maps the multiple data symbols into multiple parallel spatialstreams. For example, the modulator 730 a may generate S parallelspatial streams that may be represented by a data symbol vector x=[x₁,x₂, . . . , x_(S), and each individual symbol x_(S) in the data symbolvector x may be a symbol representative of Q transmitted bits (r_(s,1),r_(s,2), . . . , r_(s,Q)). Accordingly, a given bit r_(s,n) is the n-thbit in a data symbol of the s-th spatial stream.

For ease of explanation, in the examples presented herein, streams andsymbols have a one-to-one correspondence. That is, a single stream isassociated with a single symbol and vice versa. Accordingly, the words“streams” and “symbols” may be used interchangeably. However, it shouldbe understood that a given stream, for example, may have a number ofassociated symbols and vice versa. It should be further understood that,in some embodiments, the same symbol may be transmitted on multiplestreams.

In some embodiments, the modulator 730 a may use QAM to map bits tosymbols in a QAM signal constellation set, where the symbols aredifferentiated from one another by phase and/or magnitude, as discussed,for example, in reference to FIG. 3. However, other bit-to-symbolmappings may be utilized.

It should be noted that although the transmitting device 700 a describedwith reference to FIG. 7A includes a common encoder chain (an encoder720 a, an interleaver (not shown), a modulator 730 a, etc.), atransmitting device 700 may include different encoder chains fordifferent streams. For example, as illustrated in FIG. 7B, each streamgenerated by the transmitting device 700 b may correspond to a separateencoder chain. Other transmitting devices, such as those supporting theWiMAX standards, for example, may support both a single-encoder optionand a two-encoder option for a two-transmit-antenna configuration. Ingeneral, the number of encoders and/or encoder chains may be less thanor equal to the number of transmitted streams S.

FIG. 8 is a block diagram of an example receiving device 800 thatdemodulates received symbol data symbol vectors, accounting for channelestimation error. The receiving device 800 may be utilized in themulti-stream wireless communication system 600 as the receiving device606, for example. It will be understood, however, that the multi-streamwireless communication system 600 may alternatively use anotherreceiving device 606. Similarly, the receiving device 800 may receiveand demodulate multiple streams transmitted by a device such as thetransmitting device 700 a of FIG. 7A or the transmitting device 700 b ofFIG. 7B or some other transmitting device.

Generally, the receiving device 800 may receive information via multiplereceive antennas 802-808 and demodulate and decode the receivedinformation to estimate the information that was sent by a transmittingdevice. The receiving device 800 processes received informationutilizing a model, such as:y=(H+ΔH)x+z,  (13)where

${{y = \begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{N_{R}}\end{bmatrix}};{x = \begin{bmatrix}x_{1} \\x_{2} \\\vdots \\x_{N_{S}}\end{bmatrix}};{z = \begin{bmatrix}z_{1} \\z_{2} \\\vdots \\z_{N_{R}}\end{bmatrix}}},{{H = \begin{bmatrix}h_{1,1} & h_{1,2} & \ldots & h_{1,S} \\h_{2,1} & h_{2,2} & \ldots & h_{2,S} \\\vdots & \vdots & \vdots & \vdots \\h_{N_{R},1} & h_{N_{R},2} & \ldots & h_{N_{R},S}\end{bmatrix}};}$ ${{\Delta\; H} = \begin{bmatrix}{\Delta\; h_{1,1}} & {\Delta\; h_{1,2}} & \ldots & {\Delta\; h_{1,S}} \\{\Delta\; h_{2,1}} & {\Delta\; h_{2,2}} & \ldots & {\Delta\; h_{2,S}} \\\vdots & \vdots & \vdots & \vdots \\{\Delta\; h_{N_{R},1}} & {\Delta\; h_{N_{R},2}} & \ldots & {\Delta\; h_{N_{R},S}}\end{bmatrix}};$in which y represents, in vector from, a received signal, H represents aMIMO communication channel, x represents, in vector form, an estimatedtransmit signal, z represents a noise vector, and N_(R) is the number ofreceive antennas. More precisely, y_(j) is a received signal at antennaj, and z_(j) is noise at an antenna j. Although N_(R) is illustrated inFIG. 8 as being three, any number of multiple antennas may, in general,be utilized.

The MIMO communication channel H includes channel gain parametersh_(j,s) representing channel gain in a stream s at a receive antenna j.In at least some of the embodiments, each channel gain h_(j,s) is acomplex number that incorporates an amplitude factor and a phase shiftfactor. In other words, each h_(j,s) parameter may represent anattenuation coefficient associated with a certain propagation path asused in, for example, a Rayleigh fading channel model. The receivingdevice 400 may estimate the parameters h_(j,s), and parametersassociated with the noise z using any suitable technique, includingknown techniques.

The estimated MIMO communication channel H may also have an error ΔHassociated with it. That is, one, two, or more h_(j,s) parameter mayhave Δh_(j,s) errors associated with them.

With continued reference to FIG. 8, the receiving device 800 includes amulti-stream demodulator 842 that may provide likelihood valuesL(r_(s,1)), L(r_(s,2)), . . . , L(r_(s,Q)) for the transmitted bitsr_(s,1), r_(s,2), . . . , r_(s,Q). The receiving device 800 alsoincludes a decoder 844 that may use the likelihood values L(r_(s,1)),L(r_(s,2)), . . . , L(r_(s,Q)) provided by the multi-stream demodulator842 to estimate the transmitted bits r_(s,1), r_(s,2), . . . , r_(s,Q),and in turn, the original information bits b_(s,1), b_(s,2), . . . ,b_(s,W).

In order to provide likelihood values L(b_(s,1)), L(b_(s,2)), . . . ,L(b_(s,Q)) for the transmitted bits r_(s,1), r_(s,2), . . . , r_(s,Q),the multi-stream demodulator 842 may include a likelihood valuecalculator 854 that calculates the likelihood values L(r_(s,1)),L(r_(s,2)), . . . , L(r_(s,Q)) based at least in part on the receivedsignal y and on the estimated communication channel H. To estimate thecommunication channel H, the multi-stream demodulator 842 may include achannel estimator 848. Additionally, unlike conventional demodulators,the multi-stream demodulator 842 illustrated in FIG. 8 may include ameasure of channel estimation error generator 847 that generates ameasure of the channel estimation error ΔH so that the demodulator 842may account for that error when calculating the likelihood valuesL(r_(s,1)), L(r_(s,2)), . . . , L(r_(s,Q)). Because channel estimationerror ΔH may depend on the noise z on the channel, the multi-streamdemodulator 842 may further include a noise estimator 846 for generatingnoise estimate information, including, for example, the power σ_(z) ² ofthe noise.

The multi-stream demodulator 842, in some embodiments, or in some modesof operation, may not include one or more of the modules 846-854 or,alternatively, may not use each of the modules 846-854 in demodulatingthe received signals. Further, it will be appreciated that some of themodules 846-854 may be combined. Still further, the multi-streamdemodulator 842 and/or the receiving device 800 may include additionalcomponents and/or modules that, for ease of explanation, are not shownin FIG. 8. For example, the receiving device 800 may include adeinterleaver that rearranges scattered bits and restores the proper bitsequence, an analog RF front end that performs frequency downconversion,various filters, power amplifiers, and so on.

Different components and/or modules of the receiving device 800 may beimplemented as hardware, a processor executing software instructions, aprocessor implementing firmware instructions, or some combinationthereof. For example, some or all of the components may be customintegrated circuits, application-specific integration circuits (ASICs),etc., communicatively coupled by electrical busses. In this case, thereceiving device 800 optionally may include bypass busses (not shown) tobypass some of the components if the currently active MIMO mode does notrequire certain operations, such as processing multiple presentations ofa symbol encoded according to a space-time encoding scheme.

FIG. 9 is a flow diagram of an example demodulation method 900 that thereceiving device 800, or a similar receiving device, may use tocalculate the likelihood values L(r_(s,1)), L(r_(s,2)), . . . ,L(r_(s,Q)) of the transmitted bits r_(s,1), r_(s,2), . . . , r_(s,Q),accounting for channel estimation error. For ease of explanation, FIG. 9will be described with reference to FIGS. 6-8. It will be understood,however, that the method 900 for calculating LLRs may be utilized withsystems and devices other than those illustrated in FIGS. 6-8.

Generally speaking when the receiving device 800 may receive, over amulti-stream communication channel H, a data symbol vector y=[y₁, y₂, .. . , y_(N) _(R) ] (block 910). In other words, the receiving device 800may receive multiple data symbols y_(s) via multiple antennas 802-808 atsubstantially the same time.

In order to decode and/or demodulate the received data symbols, thereceiving device 800 may determine an estimate of the multi-streamcommunication channel H (block 920), e.g., using the channel estimator848. This estimation of the multi-stream communication channel H may beperformed in a variety of ways, including using channel estimationtechniques known in the art (e.g., least squares channel estimation,iterative channel estimation, and so on).

The receiving device 800 may then generate a measure of the channelestimation error ΔH (block 530), e.g., using measure of estimation errorgenerator 847. In one implementation, this measure may be set to thenoise power σ_(z) ², or to a scaled version of the noise power σ_(z) ².However, other values for the measure of the channel estimation error ΔHmay be used.

Once the receiving device 800 generates the measure of the channelestimation error ΔH (block 530), the receiving device 800 may determine,e.g., using the likelihood value calculator 858, likelihood values forthe bits in the transmitted symbol vector x, at least in part based onthe generated measure (block 940). This may be done, for instance, byextending equations (11)-(12) into vector form using suitable linearalgebra and other techniques

Accounting for channel estimation error ΔH may generally lead to betteraccuracy associated with LLR calculation (and, more broadly, withdemodulation and/or decoding) and result in a more optimal performancein the aggregate. For example, FIG. 10 is a graph 1000 illustrating theperformance of a simulated receiving device utilizing conventionaldemodulating techniques that do not account for channel estimation error(plot 1010) and the performance of a simulated receiving deviceutilizing demodulation techniques described herein that account forchannel estimation error (plot 1020). For this simulation, atransmitting device with 1 antenna and a receiving device with 4antennas were simulated, where the transmitting device was transmittingpackets of 1000 bytes (modulated using 64-QAM modulation) to thereceiving device. A type D, non-line of sight (DNLOS) channel model withno impairments was used, and it was assumed that σ_(h) ² was equal tothe power of the additive Gaussian noise σ_(z) ².

As illustrated in the graph 1000 in FIG. 10, for the same frame errorrate, the receiving device utilizing demodulation techniques describedherein that account for channel estimation error could operate inenvironments with a higher signal-to-noise ratio than could thesimulated receiving device utilizing conventional demodulatingtechniques that do not account for channel estimation error. Forexample, for a frame error rate of 0.08 (i.e., 8 out every 100 packetsin error), the receiving device utilizing demodulation techniquesdescribed herein, accounting for channel estimation error, could operatein environments with a 0.50-0.75 dB higher signal-to-noise ratio thancould the simulated receiving device utilizing conventional demodulatingtechniques, not accounting for channel estimation error. In general,demodulation techniques described herein that account for channelestimation error may lead to a gain performance of the order to 0.5 dBin the low to moderate signal-to-noise ratio regime.

At least some of the various blocks, operations, and techniquesdescribed above may be implemented using hardware, a processor executingfirmware instructions, a processor executing software instructions, orany combination thereof. When implemented using a processor executingfirmware or software instructions, the software or firmware may bestored in any computer readable memory such as on a magnetic disk, anoptical disk, or other storage medium, in a RAM or ROM or flash memory,processor, hard disk drive, optical disk drive, tape drive, etc.Likewise, the software or firmware may be delivered to a user or asystem via any known or desired delivery method including, for example,on a computer readable disk or other transportable computer storagemechanism or via communication media. Communication media typicallyembodies computer readable instructions, data structures, programmodules or other data in a modulated data signal such as a carrier waveor other transport mechanism. The term “modulated data signal” means asignal that has one or more of its characteristics set or changed insuch a manner as to encode information in the signal. By way of example,and not limitation, communication media includes wired media such as awired network or direct-wired connection, and wireless media such asacoustic, radio frequency, infrared and other wireless media. Thus, thesoftware or firmware may be delivered to a user or a system via acommunication channel such as a telephone line, a DSL line, a cabletelevision line, a fiber optics line, a wireless communication channel,the Internet, etc. (which are viewed as being the same as orinterchangeable with providing such software via a transportable storagemedium). The software or firmware may include machine readableinstructions that are capable of causing one or more processors toperform various acts.

Although the forgoing text sets forth a detailed description of numerousdifferent embodiments, it should be understood that the scope of thepatent is defined by the words of the claims set forth at the end ofthis patent. The detailed description is to be construed as exemplaryonly and does not describe every possible embodiment because describingevery possible embodiment would be impractical, if not impossible.Numerous alternative embodiments could be implemented, using eithercurrent technology or technology developed after the filing date of thisdisclosure, which would still fall within the scope of the claims.

What is claimed is:
 1. A method comprising: receiving a data symbol yover a communication channel, wherein the received data symbol ycorresponds to a transmitted data symbol x; processing the data symbol yaccording to a model y=(h+Δh) x+z, where h is an estimate of thecommunication channel, Δh is a channel estimation error corresponding tothe estimate h of the communication channel, and z is noisecorresponding to the communication channel, and wherein processing thedata symbol y comprises determining, with a hardware device, theestimate h of the communication channel, determining, with the hardwaredevice, a mean square error σ_(h) ² corresponding to the channelestimation error Δh, and determining, with the hardware device, alikelihood value for a bit in the transmitted data symbol x at least inpart by calculating a first quantity equal to σ_(z) ²+σ_(h) ²|x|², whereσ_(z) ² is the noise power of the communication channel, calculating asecond quantity equal to$e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}},$ and calculating the likelihood value for the bit using at least (i) thefirst quantity and (ii) the second quantity.
 2. The method of claim 1,wherein determining the likelihood value for the bit in the transmitteddata symbol x comprises calculating a log-likelihood ratio for the bit.3. The method of claim 1, wherein determining the likelihood value forthe bit comprises calculating${L(i)} = {\log\frac{\sum\limits_{x \in S_{1,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}{\sum\limits_{x \in S_{0,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, and S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to
 0. 4. The method of claim 1, whereincalculating the likelihood value for the bit comprises calculating${{L(i)}{\max\limits_{x \in S_{1,i}}{\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\underset{x \in S_{{1,i}\mspace{104mu}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)}\pi}}}} - {\underset{x \in S_{0,i}}{\max\;}\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\underset{x \in S_{{0,i}\mspace{124mu}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, and S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to
 0. 5. The method of claim 1, wherein thetransmitted data symbol x is modulated using a modulation scheme thatgenerates a plurality of constellation points, wherein at least twoconstellation points in the plurality of constellation points havedifferent amplitudes.
 6. The method of claim 5, wherein the modulationscheme is a quadrature amplitude modulation (QAM) having at least 8constellation points.
 7. The method of claim 6, wherein the modulationscheme is one of 16-QAM and 64-QAM.
 8. The method of claim 1, whereinthe communication channel comprises a plurality of spatial streams, andwherein receiving the data symbol y comprises receiving a data symbolvector, the data symbol vector comprising a plurality of data symbolsthat are received in parallel via the plurality of spatial streams,wherein the data symbol vector corresponds to a transmitted data symbolvector comprising a plurality of transmitted data symbols.
 9. The methodof claim 1, wherein the noise power of the communication channel is ascaled noise power.
 10. An apparatus comprising: a demodulatorconfigured to: receive a data symbol y over a communication channel,wherein the received data symbol y corresponds to a transmitted datasymbol x; process the data symbol y according to a model y=(h+Δh) x+z,where h is an estimate of the communication channel, Δh is a channelestimation error corresponding to the estimate h of the communicationchannel, and z is noise corresponding to the communication channel, andwherein the demodulator is configured to process the data symbol y atleast in part by determining the estimate h of the communicationchannel, determining a mean square error σ_(h) ² corresponding to thechannel estimation error Δh, and determining a likelihood value for abit in the transmitted data symbol x at least in part by calculating afirst quantity equal to σ_(z) ²+σ_(h) ²|x|², where σ_(z) ² is the noisepower of the communication channel, calculating a second quantity equalto$e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}},$ and calculating the likelihood value for the bit using at least (i) thefirst quantity and (ii) the second quantity; and a decoder configured todecode the data symbol y based at least in part on the calculatedlikelihood value.
 11. The apparatus of claim 10, wherein the demodulatoris configured to determine the likelihood value for the bit in thetransmitted data symbol x by calculating a log-likelihood ratio for thebit.
 12. The apparatus of claim 10, wherein the demodulator isconfigured to determine the likelihood value for the bit by calculating${L(i)} = {\log\frac{\sum\limits_{w \in S_{1,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}{\sum\limits_{x \in S_{0,i}}{\frac{1}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}}}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, and S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to
 0. 13. The apparatus of claim 10, whereinthe demodulator is configured to determine the likelihood value for thebit by calculating${{L(i)}{\max\limits_{x \in S_{1,i}}{\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\underset{x \in S_{{1,i}\mspace{104mu}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)}\pi}}}} - {\underset{x \in S_{0,i}}{\max\;}\log\frac{e^{\frac{- {{y - {hx}}}^{2}}{\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}}}}{\underset{x \in S_{{0,i}\mspace{124mu}}}{\left( {\sigma_{z}^{2} + {\sigma_{h}^{2}{x}^{2}}} \right)\pi}}}$where S_(1,i) is a set of all possible transmitted data symbols x withbit i equal to 1, and S_(0,i) is a set of all possible transmitted datasymbols x with bit i equal to
 0. 14. The apparatus of claim 10, whereinthe transmitted data symbol is modulated using a modulation scheme thatgenerates a plurality of constellation points, wherein at least twoconstellation points in the plurality of constellation points havedifferent amplitudes.
 15. The apparatus of claim 10 wherein the noisepower of the communication channel is a scaled noise power.